Polynomial and special function theory remains a vibrant area of mathematical research, interweaving classical algebra with advanced analysis. At its core, the study concerns algebraic expressions ...

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. In this context, the target function is often smooth and ...

This function is a polynomial in two dimensions, with terms up to degree 5. It is nonlinear, and it is smooth despite being complex, which is common for computer experiment functions (Lim et al., 2002 ...

The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focused on local polynomial smoothers.